def test_log1p_opt():
x = Symbol('x')
expr1 = log(x + 1)
opt1 = optimize(expr1, [log1p_opt])
assert log1p(x) - opt1 == 0
expr2 = log(3 * x + 3)
opt2 = optimize(expr2, [log1p_opt])
assert log1p(x) + log(3) == opt2
def test_exp2_opt():
x = Symbol('x')
expr1 = 1 + 2**x
opt1 = optimize(expr1, [exp2_opt])
assert opt1 == 1 + exp2(x)
expr2 = 1 + 3**x
assert expr2 == optimize(expr2, [exp2_opt])
def test_expm1_opt():
x = Symbol('x')
expr1 = exp(x) - 1
opt1 = optimize(expr1, [expm1_opt])
assert expm1(x) - opt1 == 0
expr2 = 3 * exp(x) - 3
opt2 = optimize(expr2, [expm1_opt])
assert 3 * expm1(x) == opt2
expr3 = 3 * exp(x) - 5
assert expr3 == optimize(expr3, [expm1_opt])
expr4 = 3 * exp(x) + log(x) - 3
opt4 = optimize(expr4, [expm1_opt])
assert 3 * expm1(x) + log(x) == opt4
def test_sin_approx():
x = Symbol('x')
expr1 = 1 + sin(x)
approx1 = optimize(expr1, [sin_approx],
bounds={x: (-.1, .1)},
reltol=1e-10,
abstol=1e-10)
assert approx1 == 1 + x - x**3 / 6 + x**5 / 120
def test_log2_opt():
x = Symbol('x')
expr1 = 7 * log(3 * x + 5) / (log(2))
opt1 = optimize(expr1, [log2_opt])
assert opt1 == 7 * log2(3 * x + 5)
expr2 = 3 * log(5 * x + 7) / (13 * log(2))
opt2 = optimize(expr2, [log2_opt])
assert opt2 == 3 * log2(5 * x + 7) / 13
expr3 = log(x) / log(2)
opt3 = optimize(expr3, [log2_opt])
assert opt3 == log2(x)
expr4 = log(x) / log(2) + log(x + 1)
opt4 = optimize(expr4, [log2_opt])
assert opt4 == log2(x) + log(2) * log2(x + 1)
expr5 = log(17)
opt5 = optimize(expr5, [log2_opt])
assert opt5 == expr5
def test_sum_approx():
x, y = map(Symbol, 'x y'.split())
expr1 = 1 + x
apx1 = optimize(expr1, [sum_approx], bounds={x: (-1e-20, 1e-20)})
assert apx1 - 1 == 0
expr2 = exp(x) + exp(y)
apx2 = optimize(expr2, [sum_approx],
bounds={
x: (0, oo),
y: (-oo, 0)
},
reltol=1e-14)
assert apx2 == exp(x) + exp(y)
apx3 = optimize(expr2, [sum_approx],
bounds={
x: (0, oo),
y: (-oo, -50)
},
reltol=1e-14)
assert apx3 == exp(x)
def test_optims_c99():
x = Symbol('x')
expr1 = 2**x + log(x) / log(2) + log(x + 1) + exp(x) - 1
opt1 = optimize(expr1, optims_c99).simplify()
assert opt1 == exp2(x) + log2(x) + log1p(x) + expm1(x)
expr2 = log(x) / log(2) + log(x + 1)
print()
opt2 = optimize(expr2, optims_c99)
assert opt2 == log2(x) + log1p(x)
expr3 = log(x) / log(2) + log(17 * x + 17)
opt3 = optimize(expr3, optims_c99)
delta3 = opt3 - (log2(x) + log(17) + log1p(x))
assert delta3 == 0
expr4 = 2**x + 3 * log(5 * x + 7) / (13 * log(2)) + 11 * exp(x) - 11 + log(
17 * x + 17)
opt4 = optimize(expr4, optims_c99).simplify()
delta4 = opt4 - (exp2(x) + 3 * log2(5 * x + 7) / 13 + 11 * expm1(x) +
log(17) + log1p(x))
assert delta4 == 0
def test_expm1_two_exp_terms():
x, y = map(Symbol, 'x y'.split())
expr1 = exp(x) + exp(y) - 2
opt1 = optimize(expr1, [expm1_opt])
assert opt1 == expm1(x) + expm1(y)